System and method for operating a three-dimensional printer to compensate for radial velocity variations

ABSTRACT

A three-dimensional object printer is configured to enable the density of material ejected by at least one printhead onto a rotating platen near its circumferential edge to be approximately the same as the density of the material ejected onto the rotating platen near the center of the platen.

TECHNICAL FIELD

This disclosure is directed to three-dimensional object printing systemsand, more particularly, to systems and methods for formingthree-dimensional objects on a rotating platen or cone.

BACKGROUND

Digital three-dimensional manufacturing, also known as digital additivemanufacturing, is a process of making a three-dimensional solid objectfrom a digital model of virtually any shape. Three-dimensional printingis an additive process in which one or more printheads eject successivelayers of material on a substrate in different shapes. Three-dimensionalprinting is distinguishable from traditional object-forming techniques,which mostly rely on the removal of material from a work piece by asubtractive process, such as cutting or drilling.

In one form of three-dimensional object printing, a radial arm on whichone or more printheads are mounted eject building or support materialonto a rotating platen or cone to form the object. The printheads ejectthe material downwardly onto the platen or cone rotating with a constantangular velocity ω. Because the outer perimeter of the rotatingstructure traverses a greater distance than the inner portions of thestructure, the outer perimeter is traveling at a greater velocity thanthe inner portion. Since the inkjets in the printhead(s) are equallyspaced at a distance Δr along the radial arm and each inkjet along theradial arm fires an ink drop having a mass m at time intervals Δt, thedensity of a solid ring formed by each inkjet is a function of itsposition along the radial arm. Thus, the density of the ring isapproximately m/(rωΔtΔr) since one can assume that Δt and Δr are bothrelatively small compared to r. The curvature effects from theseparameters are second order variations. Consequently, the density of thesolid object being formed varies primarily with the position of theinkjet along the radial arm.

One way of keeping the density constant for all inkjets along the radialarm would be to maintain the uniform radial spacing Δr and fire theouter inkjets faster than the inner inkjets. This solution is notimplemented in most inkjet printers, however, because inkjet printheadsrequire a constant firing frequency for all inkjets in the printhead.Alternatively, image processing can be designed to compensate for thedifferent radial positions and platen or cone speed differences byhalftoning the image data to equalize the density of the material ringsformed by the inkjets. This processing, however, wastes a significantamount of the throughput capability of the printheads and introducesvarious imaging artifacts.

Operating inkjet printers to reduce the variations in object materialdensity caused by variations in the radial position of the inkjets wouldbe beneficial.

SUMMARY

A three-dimensional object printer has been configured to maintain aconsistent density for material ejected by inkjets along a radial arm inthe printer. The three-dimensional object printer includes a platenconfigured to rotate about a center, a radial arm that extends from aposition proximate the center of the platen to a position proximate acircumferential edge of the platen, at least one printhead mounted tothe radial arm, the at least one printhead being configured to ejectmaterial onto the platen as the platen rotates past the at least oneprinthead, and a controller operatively connected to the at least oneprinthead and the platen, the controller being configured to rotate theplaten, operate the at least one printhead to eject material onto theplaten as the platen rotates past the at least one printhead, and movethe at least one printhead along the radial arm between a positionproximate the center of the platen to a position proximate thecircumferential edge of the platen at a linear velocity that enables aproduct of a distance of the at least one printhead from the center ofthe platen and the angular velocity of the platen to remain constant asthe at least one printhead moves between the position proximate thecenter of the platen and the position proximate the circumferential edgeof the rotating platen.

Another embodiment of the three-dimensional object printer maintains thedensity at the outer portions of the platen by decreasing the distancebetween inkjets in printheads in the printer. The printer includes aplaten configured to rotate about a center, a radial arm that extendsfrom a position over the center of the platen to a position over acircumferential edge of the platen, at least one printhead mounted tothe radial arm, the at least one printhead being configured to ejectmaterial onto the platen as the platen rotates past the at least oneprinthead, the at least one printhead being further configured with alinear array of inkjets, at least some inkjets in the linear array areseparated from one another by a decreasing distance as the linear arrayof inkjets extends towards the circumferential edge of the platen, and acontroller operatively connected to the at least one printhead and theplaten, the controller being configured to rotate the platen, andoperate the at least one printhead to eject material onto the platen asthe platen rotates past the at least one printhead.

A method of operating a three-dimensional object printer has beendeveloped that maintains a consistent density for material ejected byinkjets along a radial arm in the printer. The method includes rotatingwith a controller a platen about a center of the platen, operating withthe controller at least one printhead to eject material onto the platenas the platen rotates past the at least one printhead, and moving withthe controller at least one printhead along a radial arm that extendsfrom a position over the center of the platen to a position over acircumferential edge of the platen, the controller moving the at leastone printhead along the radial arm at a linear velocity that enables aproduct of a distance of the at least one printhead from the center ofthe platen and the angular velocity of the platen to remain constant asthe at least one printhead moves to the circumferential edge of therotating platen.

BRIEF DESCRIPTION OF THE DRAWINGS

The foregoing aspects and other features of an apparatus or printer thatmaintains a consistent density for material ejected by inkjets along aradial arm in the printer are explained in the following description,taken in connection with the accompanying drawings.

FIG. 1 is a diagram of a three-dimensional object printer having aprinthead configured to produce a consistent density of material ejectedonto a rotating platen from its center to its circumferential edge.

FIG. 2 is a diagram of another embodiment of a three-dimensional objectprinter having a printhead configured to produce a substantiallyconsistent density of material ejected onto a rotating platen from itscenter to its circumferential edge.

FIG. 3 is a diagram of another embodiment of a three-dimensional objectprinter configured to move the printhead between the center of theplaten and its circumferential edge.

FIG. 4 is a graph of the positions at which inkjets in a printhead wouldfire to eject the drops in along a radial path.

FIG. 5 is a graph of the positions at which inkjets in a printhead wouldfire to align the drops radially and provide more drops along eachsuccessive curve section.

FIG. 6 is a diagram of a prior art three-dimensional object printer thatillustrates the factors that vary the density of the material ejected bya printhead onto a rotating platen.

DETAILED DESCRIPTION

For a general understanding of the environment for the device disclosedherein as well as the details for the device, reference is made to thedrawings. In the drawings, like reference numerals designate likeelements.

As used herein, the term “build material” refers to a material that isejected in the form of liquid drops from a plurality of ejectors in oneor more printheads to form layers of material in an object that isformed in a three-dimensional object printer. Examples of buildmaterials include, but are not limited to, thermoplastics, UV curablepolymers, and binders that can be liquefied for ejection as liquid dropsfrom ejectors in one or more printheads and subsequently hardened into asolid material that forms an object through an additivethree-dimensional object printing process. In some three-dimensionalobject printer embodiments, multiple forms of build material are used toproduce an object. In some embodiments, different build materials withvarying physical or chemical characteristics form a single object. Inother embodiments, the printer is configured to eject drops of a singletype of build material that incorporates different colors through dyesor other colorants that are included in the build material. Thethree-dimensional object printer controls the ejection of drops of buildmaterials with different colors to form objects with varying colors andoptionally with printed text, graphics, or other single and multi-colorpatterns on the surface of the object.

As used herein, the term “support material” refers to another materialthat can be ejected from printheads during a three-dimensional objectprinting process to stabilize the object that is formed from the buildmaterial. For example, as the three-dimensional object printer applieslayers of the build material to form the object, at least one printheadin the printer also ejects layers of the support material that engageportions of the object. The support material holds the previously formedlayer of the build material in place, prevents newly formed featuresfrom breaking before sufficient build material is present to hold theobject together, and prevents portions of the build material that havenot fully solidified from flowing out of position before the hardeningprocess is completed. Examples of support material include, but are notlimited to, waxy materials that provide support to the object during theprinting process and that can be easily removed from the object afterthe printing process is completed.

As used herein, the term “process direction” refers to a direction ofmovement of a platen past one or more printheads during athree-dimensional object formation process. The platen holds thethree-dimensional object and accompanying support material during theprint process. In some embodiments, the platen is a planar member orconical member that rotates adjacent to or beneath one or moreprintheads on a radial arm to support the formation of an object duringthe three-dimensional object printing process.

As used herein, the term “cross-process direction” refers to a directionthat is perpendicular to the process direction and substantiallyparallel to the arrangement of at least some of the printheads thateject the drops of build material and support material to form theobject. The ejectors in two or more printheads are registered in thecross-process direction to enable an array of printheads to form printedpatterns of build material and support material over a two-dimensionalplanar region. During a three-dimensional object printing process,successive layers of build material and support material that are formedfrom the registered printheads form a three-dimensional object.

As used herein, the term “z-direction” refers to a direction ofseparation between the printheads in the three-dimensional objectprinter and the object and support material that are formed on thesupport member. At the beginning of the three-dimensional objectprinting process, the z-direction refers to a distance of separationbetween the support member and the printheads that form the layers ofbuild material and support material. As the ejectors in the printheadsform each layer of build material and support material, the z-directionseparation between the printheads and the uppermost layer decreases. Inmany three-dimensional object printer embodiments, the z-directionseparation between the printheads and the uppermost layer of printedmaterial is maintained within comparatively narrow tolerances to enableconsistent placement and control of the ejected drops of build materialand support material. In some embodiments, the support member moves awayfrom the printheads during the printing operation to maintain thez-direction separation, while in other embodiments the printheads moveaway from the partially printed object and support member to maintainthe z-direction separation.

FIG. 6 depicts a prior art three-dimensional object printer 100 thatdemonstrates the inconsistent density arising from the radial armconfiguration of the printheads. The printer 100 includes a rotatingplaten 102 and one or more printheads 112 mounted to a radial arm 108that form a linear array of inkjets 104. The inkjets in the printhead112 are a same distance from one another. A controller 130 isoperatively connected to an actuator 134 to rotate the platen 102 at apredetermined angular velocity ω. As shown in FIG. 1, drops of material116 ejected by the inkjets 104 nearer the outer end of the arm 108 areseparated by a greater distance than the material drops 116 ejected bythe inkjets nearer the origin of the radial arm at the center of theplaten 102. The longer the radial arm is, the greater the discrepancy inthe density of the lines formed by the inkjets along the length of theradial arm 108. Thus, the size of the objects that can be formed by theprinter 100 is limited by the tolerance for the discrepancy in thedensity of the material in the object from the center to its periphery.

The embodiment of an inkjet printer shown in FIG. 1 addresses the issuein density variation shown in FIG. 6. Again, the controller 130 operatesthe actuator 134 to rotate the platen 102 at a predetermined angularvelocity ω. In this embodiment, the spacing between the inkjets 104 inthe linear array of inkjets formed by the one or more printheads 112mounted to the radial arm 108 is not the same distance. Instead, theinkjets nearer the outer end of the radial arm are positioned closertogether than the inkjets nearer the center of the platen. Thisvariation in the distance between inkjets enables the drops from theinkjets to remain aligned along a radial as shown in FIG. 4. In oneembodiment, the inkjets along the inner half of the radial arm areseparated by a distance corresponding to 300 dpi, while the inkjetsalong the outer half of the radial arm are separated by a distancecorresponding to 600 dpi. In another embodiment, the distance betweeneach inkjet varies with each inkjet being closer to the next adjacentinkjet towards the outer end of the radial arm than the inkjet is to thenext adjacent inkjet towards the inner end of the radial arm.

In the embodiment shown in FIG. 2, the controller 130 operates theactuator 134 to rotate the platen 102 at a predetermined angularvelocity ω. An inner printhead 120 is positioned to extend radiallyalong the arm 108, and an outer printhead 124 is tilted at an angle withrespect to the arm 108. The inkjets 104 in both printheads are separatedby the same distance in the cross-process direction across the width ofthe printheads. By tilting the printhead 124 with respect to the radialarm 108, however, the inkjets in printhead 124 eject material dropscloser to one another than they would if the printhead 124 was alignedradially with the arm 108.

In the printer configuration of FIG. 3, the printhead 120 is mounted tothe radial arm 108 and operatively connected to an actuator 138, whichis operatively connected to the controller 130, to enable the controller130 to move the printhead 120 radially along the arm 108 between thecenter of the platen 102 and its circumferential edge. Again, thecontroller 130 operates the actuator 134 to rotate the platen 102 at anangular velocity ω with reference to an electrical signal generated bythe controller 130. As explained below, the controller is configured to(1) alter the angular velocity of the platen as the printhead 120 movesbetween the center of the platen and the circumference of the platen,(2) vary the linear speed of the printhead along the radial arm, or (3)alter the tilt of the printhead as it moves along the radial arm.Alternatively, the controller 130 can be configured to perform somecombination of these operations to help maintain the density of thematerial rings being formed until the object formation is completed.

In the first type of operation, the controller 130 moves the printheadby operating the actuator 138 and as the printhead position changes, thecontroller operates the actuator 134 to vary the angular velocity of therotating platen 102 with reference to the position of the printhead.This change in the angular velocity of the platen 102 enables thedensity of the material ejected by the printhead 120 to remainapproximately constant. One way of maintaining a consistent density isto keep the product of the radial position r of the printhead along thearm 108 and the angular velocity ω of the platen a constant. Thus, as rincreases with the outward movement of the printhead 120 along theradial arm 108, the controller reduces the angular velocity of theplaten so the product of the new radial position and the new angularvelocity is approximately equal to the product of the radial position ata prior position and previous angular velocity.

As used in this document with reference to the product noted above, theterm “constant” means the product does not vary from one printheadlocation to another by an amount that is more than a ratio between theradii near the circumferential edge and near the center of the platen.This tolerable range in density arises from the printhead having alength in the radial direction. When the spacing between the inkjets isthe same and the printhead is held at a particular location, the platentravels past the end of the printhead closest to the circumferentialedge at a higher speed than the platen portion passing the end of theprinthead closest to the center of the platen. Thus, the product beingheld “constant” refers to the radial distance and angular velocityproduct being such that the density of the material ejected at the endof the printhead at the circumferential edge of the platen approximatesthe density of the material ejected at the end of the prinhead proximatethe center of the platen. This approximate density, which does notexceed a ratio of the radii between the inner part of the printheadproximate the center of the platen and the outer part of the printheadproximate the circumferential edge, can be expressed as [(Outerradius/Inner radius)+1]/2.As used in this definition, the inner partrefers to a portion closer to the center than the outer part. That is,the “inner” part does not necessarily have to be close to the center andthe “outer” part is not required to be near the circumferential edge.Instead, one portion is relatively closer to the center than the otherportion. Thus, the ratio of the outer radius to the inner radius canapproach 1.

In the second type of operation, the controller 130 is configured tovary a speed of the printhead 120 as it moves continuously along theradial arm 108. In this embodiment, the controller 130 operates theactuator 138 to vary the linear velocity of the printhead 120 along theradial arm 108 as the printhead moves along the radial arm between aposition near the center of the platen to a position near thecircumferential edge. Additionally, the controller 130 also operates theactuator 134 to maintain the angular velocity of the rotating platen 102at the same speed. To implement this approach, the image data for theobject to be printed by the three-dimensional object printer isprocessed into concentric cylinders in a known manner. The width of eachcylinder and the number of dots per inch to be printed in thecircumference of the cylinder is a function of the radial position ofthe printhead with reference to the center of the platen and the printerarchitecture. In a variation of this embodiment, the data for operatingthe at least one printhead is generated to enable a product of a radialposition of a circumference of each cylinder and a change incircumference between a previous cylinder and a current cylinder toremain constant. The cylindrical rings decrease in width linearly as afunction of the radial position of the printhead as in the case in whicha single printhead spans the print zone from the center of the platen toits outer edge. In a printer having a single printhead that does notspan the print zone across the platen 102 and that moves outwardly toeject material at positions to enable interleaving of the materialdrops, the angular velocity of the platen is varied in addition to theprinthead radial velocity by using an average width for all of theconcentric rings. A graph depicting this relationship in this embodimentof a three-dimensional object printer is shown in FIG. 5. As shown inthe figure, not only do the ink drops align radially, as is the case inFIG. 4, but more drops are provided along each successive curve section.

In the third type of operation, the controller is configured to operateactuator 138 to tilt the printhead 120 as the controller moves theprinthead along the radial arm 108 to change the effective distancebetween the drops ejected by the printhead. As already noted withreference to the embodiment in FIG. 1, this tilting of the printheadenables the material to be ejected from the printhead at a higherresolution than when the printhead is aligned with the radial arm.

In the three types of operation that move the printhead along the radialarm, the controller can move the printhead in a discrete manner, acontinuous manner or a combination of those two movements. Also, aspreviously noted, the controller 130 can be configured to perform acombination of the three types of operation for moving the printheadalong the radial arm. Additionally, the controller can be furtherconfigured to vary the angular velocity of the platen during these threetypes of operation or any combination thereof to help maintain aconsistent density in the ejected material regardless of the location ofthe material on the platen.

In some embodiments, the controller 130 is configured to operate theplaten and the printhead in an interleaved mode and in otherembodiments, the controller 130 is configured to operate the platen in asingle pass mode. In the interleaved mode, the controller 130 operatesthe actuator 138 to move the printhead 120 incrementally upon thecompletion of each platen revolution so any particular position on theplaten can pass by the printhead more than once. This interleaved modeenables resolution of the material drops on the platen to be higher thanis possible from the inkjet spacing in the printhead alone. In thesingle pass mode, the controller 130 operates the actuator 138 to movethe printhead 120 so each position on the platen passes the printheadonly once.

The operation of the printer has been described above with reference tothe printhead being moved between a position proximate the center of theplaten and a position proximate the circumferential edge of the platen.The reader should note that the controller 130 can be configured forbi-directional movement of the printhead. In general, the controllerdecreases the speed of the printhead and/or the angular velocity of theplaten as the printhead travels outwardly from the center, and thecontroller increases the speed of the printhead and/or the angularvelocity of the platen as the printhead travels inwardly towards theplaten center. Thus, the controller 130 is configured to move theprinthead and regulate the angular velocity of the platen and linearspeed of the printhead as the printhead travels between the positionproximate the center of the platen and the position proximatecircumferential edge of the platen regardless of the direction in whichthe printhead is moving. Additionally, the controller can vary the tiltof the printhead to increase the resolution of the ejected drops as theprintheads moves outwardly and to decrease the resolution as theprinthead moves inwardly.

While the printer configurations described above reduce the differencein density between ink drops ejected closed to the inner end of theradial arm and those ejected closer to the circumferential edge, othertechniques in the processing of the image data can further enhance thiseffect. For example, the rendered image data, such as halftone data,which is used to operate the printhead(s) on the radial arm can bemanipulated to reduce the difference in density of the material on theplaten between the inner and outer portions underlying the radial arm.Other rendered image data processing can be used as well to takeadvantage of the structural configurations described above.

It will be appreciated that variants of the above-disclosed and otherfeatures and functions, or alternatives thereof, may be desirablycombined into many other different systems, applications or methods.Various presently unforeseen or unanticipated alternatives,modifications, variations or improvements may be subsequently made bythose skilled in the art that are also intended to be encompassed by thefollowing claims.

What is claimed:
 1. A three-dimensional object printer comprising: aplaten configured to rotate about a center; a first actuator operativelyconnected to the platen, the first actuator being configured to rotatethe platen; a radial arm that extends from a position proximate thecenter of the platen to a position proximate a circumferential edge ofthe platen; at least one printhead mounted to the radial arm, the atleast one printhead being configured to eject material onto the platenas the platen rotates past the at least one printhead; a second actuatoroperatively connected to the at least one printhead, the second actuatorbeing configured to move the at least one printhead along the radial armand to change an angle between the at least one printhead and the radialarm; and a controller operatively connected to the at least oneprinthead, the first actuator, and the second actuator, the controllerbeing configured to: operate the first actuator to rotate the platen;operate the at least one printhead to eject material onto the platen asthe platen rotates past the at least one printhead; and adjust operationof the first actuator to change an angular velocity of the platen oradjust operation of the second actuator to change a velocity of the atleast one printhead along the radial arm or an angle between the atleast one printhead and the radial arm to maintain a density of thematerial ejected onto a portion of the rotating platen nearer a centerof the platen constant with a density of the material ejected onto aportion of the rotating platen nearer a circumferential edge of theplaten.
 2. The printer of claim 1, the controller being furtherconfigured to: adjust operation of the second actuator to move the atleast one printhead along the radial arm between a position nearer thecenter of the platen and a position nearer the circumferential edge ofthe platen at a velocity that enables a product of a radial distance ofthe at least one printhead from the center of the platen and the angularvelocity of the platen to remain constant as the at least one printheadmoves between a position nearer the center of the rotating platen and aposition nearer the circumferential edge of the rotating platen.
 3. Thethree-dimensional object printer of claim 2, the controller beingfurther configured to: operate the first actuator to rotate the platenat a predetermined angular velocity; and adjust operation of the secondactuator to reduce the velocity of the at least one printhead as the atleast one printhead moves towards the position nearer thecircumferential edge of the platen to maintain the product of the radialdistance of the at least one printhead from the center of the platen andthe angular velocity of the platen constant as the at least oneprinthead moves towards the position nearer the circumferential edge ofthe rotating platen.
 4. The three-dimensional object printer of claim 2,the controller being further configured to: operate the first actuatorto rotate the platen at a predetermined angular velocity; and adjustoperation of the second actuator to increase the velocity of the atleast one printhead as the at least one printhead moves towards theposition nearer the center of the platen to maintain the product of theradial distance of the at least one printhead from the center of theplaten and the angular velocity of the platen constant as the at leastone printhead moves towards the position nearer the center of therotating platen.
 5. The three-dimensional object printer of claim 1, thecontroller being further configured to: adjust operation of the firstactuator to adjust the angular velocity of the rotating platen as the atleast one printhead moves between a position nearer the center of theplaten and a position nearer the circumferential edge of the platen tomaintain a product of a radial distance of the at least one printheadfrom the center of the platen and the angular velocity of the platenconstant as the at least one printhead moves between the position nearerthe center of the platen and the position nearer the circumferentialedge of the rotating platen.
 6. The three-dimensional object printer ofclaim 5, the controller being further configured to: adjust operation ofthe first actuator to increase the angular velocity of the rotatingplaten as the at least one printhead moves from the position nearer thecircumferential edge of the platen towards the position nearer thecenter of the platen to maintain the product of the radial distance ofthe at least one printhead from the center of the platen and the angularvelocity of the platen constant as the at least one printhead movestowards the position nearer the center of the rotating platen.
 7. Thethree-dimensional object printer of claim 5, the controller beingfurther configured to: adjust operation of the first actuator todecrease the angular velocity of the rotating platen as the at least oneprinthead moves from the position nearer the center of the platentowards the position nearer the circumferential edge of the platen tomaintain the product of the radial distance of the at least oneprinthead from the center of the platen and the angular velocity of theplaten constant as the at least one printhead moves towards the positionnearer the circumferential edge of the rotating platen.
 8. Thethree-dimensional object printer of claim 1, the controller beingfurther configured to: adjust operation of the second actuator to rotatethe at least one printhead with respect to the radial arm to increase anangle between the at least one printhead and the radial arm as the atleast one printhead moves towards the circumferential edge of theplaten.
 9. The three-dimensional object printer of claim 1, thecontroller being further configured to: adjust operation of the secondactuator to rotate the at least one printhead with respect to the radialarm to decrease an angle between the at least one printhead and theradial arm as the at least one printhead moves towards the center of theplaten.
 10. The three-dimensional object printer of claim 5, thecontroller being further configured to: generate data for operating theat least one printhead from image data corresponding to an object to beproduced by the three-dimensional object printer, the data for operatingthe at least one printhead corresponding to a plurality of cylindersconcentric with the center of the platen; and operate the first actuatorand the second actuator with reference to the generated data.
 11. Thethree-dimensional object printer of claim 10, the controller beingfurther configured to: generate the data for operating the at least oneprinthead to enable a product of a radial position of a circumference ofeach cylinder and a change in circumference between a previous cylinderand a current cylinder being a constant.
 12. The three-dimensionalobject printer of claim 1, the at least one printhead being configuredas at least two printheads mounted to the radial arm, the inkjets withineach of the at least two printheads being separated from one another ina direction aligned with the radial arm by a same distance, one of theat least two printheads being nearer the center of the platen and beingaligned with the radial arm and another of the least two printheadsbeing nearer the circumferential edge and being at an angle withreference to the radial arm to enable the inkjets in the other printheadnearer the circumferential edge to eject material drops at a densityconstant with a density for the material drops ejected by the printheadnearer the center of the platen.